Answer:
2[tex]\sqrt{5}[/tex]
Step-by-step explanation:
Using the rule of radicals
[tex]\sqrt{a}[/tex] × [tex]\sqrt{b}[/tex] ⇔ [tex]\sqrt{ab}[/tex]
Simplifying the radicals
[tex]\sqrt{125}[/tex] = [tex]\sqrt{25(5)}[/tex] = [tex]\sqrt{25}[/tex] × [tex]\sqrt{5}[/tex] = 5[tex]\sqrt{5}[/tex]
[tex]\sqrt{180}[/tex] = [tex]\sqrt{36(5)}[/tex] = [tex]\sqrt{36}[/tex] × [tex]\sqrt{5}[/tex] = 6[tex]\sqrt{5}[/tex]
[tex]\sqrt{45}[/tex] = [tex]\sqrt{9(5)}[/tex] = [tex]\sqrt{9}[/tex] × [tex]\sqrt{5}[/tex] = 3[tex]\sqrt{5}[/tex]
Thus
[tex]\sqrt{125}[/tex] - [tex]\sqrt{180}[/tex] +[tex]\sqrt{45}[/tex]
= 5[tex]\sqrt{5}[/tex] - 6[tex]\sqrt{5}[/tex] + 3[tex]\sqrt{5}[/tex]
= 2[tex]\sqrt{5}[/tex]
